Make a copy while the list is still there
Open My List and choose Create backup. Copy the complete text from the backup box and keep it somewhere you control. It contains movie and series references plus valid manual checkpoints, not passwords, playable videos or a synchronized profile. Create the copy before clearing site data or replacing a browser.
Merge rather than replace
In another browser, open My List on this same website and paste the text into Restore backup. Merge adds known saved titles and valid checkpoints. Existing checkpoints in that browser are kept, so a backup does not unexpectedly move a series backward. Unknown records and invalid episode numbers are skipped rather than converted into invented titles.
Keep the boundaries understandable
A list saved under another website's address is a separate list. Private windows and browser profiles can also have different storage. If a browser blocks saving, the page reports that problem instead of pretending your choice will survive. There is no server account to recover a list after the only copy has been erased.